An endofunctor \(\mathcal {G}\)  on the category of measurable spaces \(\textbf {Mble}\)  can be defined by sending a measurable space \(X\)  to the measurable space of all probability measures on \(X\) . Using Dirac delta probability measures and integration, this endofunctor can be given a monad structure. This monad is called the Giry monad [1]}. Monads on categories of measurable and topological spaces that are similar to the Giry monad are referred to as probability monads.
